
where \(\beta \colon \Sigma _g M \rightarrow \Sigma _{\widetilde{g}} M\)  is the induced isometric isomorphism between the spinor bundles associated to the different metrics \(g\)  and \(\widetilde{g}\)  respectively [1]}, [2]}, then
\(&K_{\widetilde{g}}= e^{-2w}(K_g- \Delta _g w), \ \ &\Delta _{\widetilde{g}} u_j= e^{-2w} \Delta _{g} u_j, \quad j=1,2\) 
